A gas occupied $360 c m^{3}$ at $87^{\circ} C$ and 380 mm Hg pressure. If the mass of gas is 0.546 g find its relative molecular mass.

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Solution

Find the relative molar mass of the given gas

$R e l a t i v e M o l a r m a s s o f t h e g a s = \frac{D e n s i t y \times R \times T e m p e r a t u r e}{P r e s s u r e}$

Temperature = $87^{\circ} C + 273 K = 360 K$

Pressure = $\frac{380 m m H g}{760 m m H g / a t m} = 0.5 a t m$

Volume = $360 m l = 0.360 L$

Density = $\frac{m a s s}{v o l u m e}$ = $\frac{0.546 g}{0.360 L} = 1.52 g / L$

$R e l a t i v e M o l a r m a s s o f t h e g a s = \frac{1.52 g / L \times 0.0821 a t m L / m o l K \times 360 K}{0.5 a t m} = 89.85 g / m o l$

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